"I have a blue coat."
Translation:عِنْدي مِعْطَف أَزْرَق.
Well ... there is no specific rule really .. but there are hints ... the rest is a work of memory as you need to memorize the feminine and masculine nouns.
many times, feminine words would end in Ta-Marbútah ة - but there are also nouns that are feminine without it (e.g. šams شمس: sun).
There are words that are a bit controversial so using feminine or masculine is alright, e.g. knife: سكين (sikkeen: can be considered masculine or feminine) or سكينة (sikkeenah) (can be feminine only).
No not a dialect .. in fact .. i do indeed prefer ليس لدي rather than ليس عندي ..... though both are correct but some scholars do explain a delicate difference between the two. Anyway, no need to delve deep into these delicate expressions, but generally speaking both expressions are correct